Answer:
The sequence diverges.
Step-by-step explanation:
A sequence [tex]a_{n}[/tex] converges when [tex]\lim_{n \rightarrow \infty} a_{n}[/tex] is a real number.
In this question, the sequence given is:
[tex]a_{n} = 4n\cos{(7n\pi)}[/tex]
The cosine is always going to be between -1 and 1, so for the convergence of the sequence, we look it as: [tex]a_{n} = 4n[/tex]. So
[tex]\lim_{n \rightarrow \infty} a_{n} = \lim_{n \rightarrow \infty} 4n = \infty[/tex]
Since the limit is not a real number, the sequence diverges.
